Háskóli Íslands
Raunvísindadeild,
Physical chemistry B / EFN403G
Spectrum of the Hydrogen Atom
INTRODUCTION / THEORY
The emission of the hydrogen lamp:
The emission spectrum of the hydrogen atom is the best known atomic spectrum. The
spectrum was useful for N. Bohr, when he build his model and theory about quantum
mechanics for atoms about a decade ago.
The quantized energy for the H atom (E(n)) can be expressed as
E ( n)  
R
( J ); R  Rydberg cons tan t ( J )
n2
(1)
The spectrum is due to energy transfers between energy levels where the energy of the
emitted photons(Elight =h; h: Planck const, : freq.) equals the energy difference between
quantum levels n1 and n2:
1 1
Elight h  R  2  2 
 n2 n1 
~
Elight  hc(1 /  )  hc~ ;
(2)
~  Elight / hc
(3)
c: speed of light, ~ : the photon wavenumber (cm-1). According to (2) and (3),
~ 1 1 
 2 ;
2
 n2 n1 
~  R 
~
R  109737.31534 cm1
Spectra lines due to transitions from quantum levels n1 = 3,4, ... to n2 = 2 are named Balmer
lines and appear in the visible spectral region.
If you plot up ~ as a function of
1
the Rydberg constant () can be obtained from the
n12
slope of a line fit as described in supporting material /
http://www3.hi.is/~agust/kennsla/ee10/eeb/H-emission/H-emission-2.pdf.
Experimental technique:
The experiment is performed in VRI-121:
Fig. 1. Equipments for recording emission spectra..
The equipment consists of (Fig. 1):
–a monochromator (í: Ljósgreiða; see Figure)) (sjá nánar neðar)
–a photomultiplier (í: Ljósmagnari)) for converging light signal to electric signal.
–a high voltage Power supply for the photomultiplier.
–an integrator (í: Smali) (and power supply; í: Aflgjafi fyrir smala) for magnifying the
signal from the photomultiplier.
5) –a computer (í: Tölva) for data sampling and manipulation of the data.
6) –Control unit for the monochromator (í: stjórneining fyrir ljósgreiðu).
1)
2)
3)
4)
A monochromator consist of optics for dispersing the light emitted from the light source
(lamp) to obtain the the emission intensity as a function of wavelength (see Fig. 2).
Fig. 2. Monochromator / Digikrom 240
Initially the light from the light source is directed through an adjustable entrance slit. After
reflections by mirrors M1 and C (see Fig. 2) the light hits a grating (G) which function is to
disperse the light. After that the light is reflected via mirrors F and M2 and directed through
an adjustable exit slit to the photomultiplier. The angle of the grating determines the
wavelength which reaches the photomultiplier surface. The spectrometer resolution is
determined by the slit widths. The smaller slit width a better resolution is obtained.
Procedure:
measurements and data sampling:
A detailed description of the procedure is to be found at:
http://www3.hi.is/~agust/kennsla/ee10/eeb/H-emission/H-emission-3e.pdf
Analysis:
~
1) Determine the Rydberg constant ( R )and the ionization potential for the Hydrogen
atom (see Introduction above and description in supporting material /
http://notendur.hi.is/agust/kennsla/ee10/eeb/H-lampi-fylgigogn-311209.pdf).
2) Determine the energies () of the quantum levels involved in the electron transfer
processes of concern.
3) Compare your results with literature values2).
See pictures: http://www3.hi.is/~agust/kennsla/ee10/eeb/H-emission/H-lamp10.htm
Hand in reports no later than two weeks after you perform the experiment.
References:
1) Physical chemistry for the chemical and biochemical sciences by Raymond Chang, (2000),
chapter 14.4. page 567.
2) Database: http://physics.nist.gov/PhysRefData/ASD/index.html
3) Experiments in Physical Chemistry by D.P. Shoemaker, C.W. Garland and
J.W. Nibler, 5th edition. Mc Graw Hill
Ágúst Kvaran
H-emission-1e.doc/pdf
Edition 170111